Fermat's principle
Light travels between two points along the path that takes the least time.
Definition
Stated by Pierre de Fermat in 1662, this was the first variational principle in physics. From it alone — without any assumption about whether light is a particle or a wave — one can derive Snell's law of refraction, the straight-line propagation of light in a uniform medium, and the reflection law for mirrors.
Writing the total travel time as a functional of the path and demanding that it be stationary gives, at any interface between two media of speeds v₁ and v₂, the condition sin θ₁ / v₁ = sin θ₂ / v₂, which is Snell's law. Fermat's principle was the direct conceptual precursor of Maupertuis's principle of least action; it generalises, in modern optics, to the principle of stationary optical path length.